29

System Described by Differential Equations

• The response of many physical systems can be described by differential equations• Linear, Constant-Coefficient Differential Equations

• To solve the equation, one needs the N initial conditions y(t0), y’(t0)…y(N-1) (t0)

1

0 01

0 0

( ) ( ) ( )

( ) ( ) ( ) ( )

N i iN M

i iN i ii i

N MN i i

i ii i

d y t d y t d x ta bd t d t d t

D a D y t b D x t

−

= =

−

= =

+ =

+ =

∑ ∑

∑ ∑

Simulation Diagrams for

Continuous-Time Systems

First Canonical Form

Second Canonical Form